I didn't have time to go through the whole series (or even the first episode), but some comments on the first 20 or so minutes:

1) This may be nit-picking but Iberians are NOT the descendants of the Visigoths. Genetic studies clearly demonstrate that the Visigoths had a negligible impact on the genetic composition of Iberians and the Suebi only slightly more so (specifically in the areas of Northern Portugal and Galicia, which was historically their territory).

2) He is absolutely right to trace the origins of the Age of Discovery to the Reconquista. You can't understand the former without the latter, at all. This is something modern historians, especially those who are not hispanists, completely fail to grasp. In short: the underlying spirit of the Reconquista and the Age of Discovery is the same. Once the Reconquista drew to a close, the same zeal which sustained it for centuries was converted into a zeal to perpetuate the struggle abroad.

3) Mr. Wuest's account of what happened in 711 is pretty questionable. Here are some issues I have:

We don't know anything, really, about Tariq ibn Ziyad. All of the information we have about him, much like the information we have about D. Pelayo, is later tradition. We cannot say that he was an Arab. He may have been, but he may have been a Berber and, strange as it may sound, I've even seen it proposed that he was a Visigoth.

The treason of the Visigoths is massively, massively downplayed, here. Tariq won at Guadalate (which may not have been a battle at all) because an entire wing of Roderic's army supposedly fled the field. These were the supporters of Witiza who regarded Roderic as an usurper.

It is at least possible that the Witizans actually hired Tariq ibn Ziyad's Berbers as mercenaries in a coup agains Roderic and his supporters. This is a view that a number of hispanists take. By their analysis, Tariq didn't so much lay siege to Toledo as had the gates thrown open by the Witizans who promptly slew the Rodericans in the city.

I think he may have confused Alfonso I for D. Pelayo, the latter traditionally being credited with the foundation of the Kingdom of Asturias and the beginning of the Reconquista at Covadonga in 722.

4) Access to trade goods was an important factor in the Age of Discovery but there was little interest in Africa. The interest was in the Indies and getting around the Venetian and Mamluk monopoly on Oriental trade. In this respect, Africa was regarded as little more than an obstacle.

In addition, to say that the Age of Discovery was "precisely" because of this pursuit of new markets is a gross simplification, and not an especially accurate one. In my view, the single most important factor was the perpetuation of the Reconquista. Look at how central the search for Prester John was to Infante Henrique and his colleagues at Sagres. He was quite literally obsessed with finding the fabled king. It's true that Prester John was rumoured to be wealthy, and this was no doubt of some importance, but the real hope was that he would be a valuable and powerful ally against the Moors.

I'm going to try to listen to the rest of the series over next couple of weeks. The above may seem harshly critical, but to be fair to the author he did admit that the Medieval period was a weak point for him.